How to check the GM factory status of your order using the Chevy website:

You will need your order number.
The order number consists of 6 letters and/or numbers.
Your salesperson should be able to provide you with this number.

Go to Chevrolet.com.
If you have already set up an account, sign in up in the top right corner. If you don't have an account I would suggest that you sign up for one. I am not sure that you need an account, but I suspect the navigating the site is quicker with one. They are free.

A few seconds after you sign in a chat box will appear in the bottom right corner of the page.

This is the kicker:
Click on the chat box and type "hi" to activate the bot.
Just do it, otherwise, it'll terminate the session.

It will give you a partial list of services that it can provide.
Type: "Order Status XXXXXX" with your order number replacing, of course, the Xs in the example. Don't include any quote marks.

The bot will tell you that it is looking up your order number, and then a few seconds later it will provide that status.

In my case it told me:
"Congratulations! Your vehicle has been produced. It is important to know that shipping arrangements will take place next and your selling dealer is the best source for additional detail on that process."